We propose a model explaining the spiraling and intertwining circles illusions of Pinna & Gregory (2002). The spiral illusion is produced by a series of concentric circles, each composed of alternating black and white outlines of squares whose sides are aligned with the tangent of the circle. Rotating every square by 45 degrees in every other circle leads to a different illusion of intertwining circles. While the physical difference between the two illusions is a subtle change in orientation, the perceptual difference is great. Pinna & Gregory (2002) suggested that these illusions may result from interactions between long and short range integration. However, the illusion is absent at fixation, suggesting the effect is due to mechanisms of peripheral vision.

We have previously modeled visual crowding, a key aspect of peripheral vision, with a texture processing model (Balas, Nakano, & Rosenholtz, in submission). This model represents visual stimuli by joint statistics of cells sensitive to different position, phase, orientation, and scale. We suggest that the Pinna & Gregory illusions might be a natural by-product of this sort of statistical representation in peripheral vision.

Using (Portilla & Simoncelli, 2000) we can synthesize images which are constrained to share the same joint statistics as those computed. We call these images “mongrels”. Our hypothesis is that these mongrels are, approximately, “samples” of peripheral percepts of the stimuli. Do mongrels of these illusory stimuli predict the illusory percepts? Subjects marked contours on mongrels from the spiral and intertwining illusions, or from a control image of concentric circles made of only white squares. Their markings corresponded to the perception of spirals, many intersecting contours, or concentric circles, respectively. This suggests that the model makes accurate perceptual predictions for these illusions, and provides a method to peek into a possible representation of visual information in the periphery.